Average Error: 0.1 → 0.1
Time: 7.8s
Precision: 64
\[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
↓
\[\left(a - \frac{1}{3}\right) \cdot 1 + \left(a - \frac{1}{3}\right) \cdot \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\]
\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)
↓
\left(a - \frac{1}{3}\right) \cdot 1 + \left(a - \frac{1}{3}\right) \cdot \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}
double f(double a, double rand) {
        double r77746 = a;
        double r77747 = 1.0;
        double r77748 = 3.0;
        double r77749 = r77747 / r77748;
        double r77750 = r77746 - r77749;
        double r77751 = 9.0;
        double r77752 = r77751 * r77750;
        double r77753 = sqrt(r77752);
        double r77754 = r77747 / r77753;
        double r77755 = rand;
        double r77756 = r77754 * r77755;
        double r77757 = r77747 + r77756;
        double r77758 = r77750 * r77757;
        return r77758;
}
↓
double f(double a, double rand) {
        double r77759 = a;
        double r77760 = 1.0;
        double r77761 = 3.0;
        double r77762 = r77760 / r77761;
        double r77763 = r77759 - r77762;
        double r77764 = r77763 * r77760;
        double r77765 = rand;
        double r77766 = r77760 * r77765;
        double r77767 = 9.0;
        double r77768 = r77767 * r77763;
        double r77769 = sqrt(r77768);
        double r77770 = r77766 / r77769;
        double r77771 = r77763 * r77770;
        double r77772 = r77764 + r77771;
        return r77772;
}

Error

Bits error versus a

Bits error versus rand

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(a - \frac{1}{3}\right) \cdot \left(1 + \frac{1}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}} \cdot rand\right)\]
  2. Using strategy rm

  3. Applied associate-*l/0.1

    \[\leadsto \left(a - \frac{1}{3}\right) \cdot \left(1 + \color{blue}{\frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}}\right)\]
  4. Using strategy rm

  5. Applied distribute-lft-in0.1

    \[\leadsto \color{blue}{\left(a - \frac{1}{3}\right) \cdot 1 + \left(a - \frac{1}{3}\right) \cdot \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}}\]

  6. Final simplification0.1

    \[\leadsto \left(a - \frac{1}{3}\right) \cdot 1 + \left(a - \frac{1}{3}\right) \cdot \frac{1 \cdot rand}{\sqrt{9 \cdot \left(a - \frac{1}{3}\right)}}\]

Reproduce

herbie shell --seed 2020100 
(FPCore (a rand)
  :name "Octave 3.8, oct_fill_randg"
  :precision binary64
  (* (- a (/ 1 3)) (+ 1 (* (/ 1 (sqrt (* 9 (- a (/ 1 3))))) rand))))